Pinching rules in the chiral-splitting description of one-loop string amplitudes

Authors: Filippo Maria Balli, Alex Edison, Oliver Schlotterer

Preprint number: UUITP-30/24

Abstract: Loop amplitudes in string theories reduce to those of gauge theories and (super)gravity in their worldline description as the inverse string tension α' tends to zero. The appearance of reducible diagrams in these α' → 0 limits is determined through so-called pinching rules in the worldline literature. In this work, we extend these pinching rules to the chiral-splitting description of one-loop superstring amplitudes where left- and right-moving degrees of freedom decouple at fixed loop momentum. Starting from six points, the Kronecker-Eisenstein integrands of chiral amplitudes introduce subtleties into the pinching rules and integration-by-parts simplifications. Resolutions of these subtleties are presented and applied to produce a new superspace representation of the six-point one-loop amplitude of type IIA/B supergravity. The worldline computations and their subtleties are compared with the ambitwistor-string approach to one-loop field-theory amplitudes where integration-by-parts manipulations are shown to be more flexible. Throughout this work, the homology invariance of loop-momentum dependent correlation functions on the torus is highlighted as a consistency condition of α' → 0 limits and their comparison with ambitwistor methods.